Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1238 prodotti
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78/2024 - 16/10/2024
Ziarelli, G.; Pagani, S.; Parolini, N.; Regazzoni, F.; Verani, M.
A model learning framework for inferring the dynamics of transmission rate depending on exogenous variables for epidemic forecasts | Abstract | | Recent advancements in scientific machine learning offer a promising framework to integrate data within epidemiological models, offering new opportunities for the implementation of tailored preventive measures and the mitigation of the risks associated with epidemic outbreaks. Among the many parameters to be calibrated and extrapolated in an epidemiological model, a special role is played by the transmission rate, whose inaccurate extrapolation can significantly impair the quality of the resulting forecasts. In this work, we aim to formalize a novel scientific machine learning framework to reconstruct the hidden dynamics of the transmission rate, by incorporating the influence of exogenous variables (such as environmental conditions and strain-specific characteristics). We propose an hybrid model that blends a data-driven layer with a physics-based one. The data-driven layer is based on a neural ordinary differential equation that learns the dynamics of the transmission rate, conditioned on the meteorological data and wave-specific latent parameters. The physics-based layer, instead, consists of a standard SEIR compartmental model, wherein the transmission rate represents an input. The learning strategy follows an end-to-end approach: the loss function quantifies the mismatch between the actual numbers of infections and its numerical prediction obtained from the SEIR model incorporating as an input the transmission rate predicted by the neural ordinary differential equation. We validate this novel approach using both a synthetic test case and a realistic test case based on meteorological data (temperature and humidity) and influenza data from Italy between 2010 and 2020. In both scenarios, we achieve low generalization error on the test set and observe strong alignment between the reconstructed model and established findings on the influence of meteorological factors on epidemic spread. Finally, we implement a data assimilation strategy to adapt the neural equation to the specific characteristics of an epidemic wave under investigation, and we conduct sensitivity tests on the network’s hyperparameters. |
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77/2024 - 16/10/2024
Piersanti, R.; Bradley, R.; Ali, S.Y.; Quarteroni A.; Dede', L; Trayanova, N.A.
Defining myocardial fiber bundle architecture in atrial digital twins | Abstract | | A key component in developing atrial digital twins (ADT) - virtual representations of patients’ atria - is the accurate prescription of myocardial fibers which are essential for the tissue characterization. Due to the difficulty of reconstructing atrial fibers from medical imaging, a widely used strategy for fiber generation in ADT relies on mathematical models. Existing methodologies utilze semi-automatic approaches, are tailored to specific morphologies, and lack rigorous validation against imaging fiber data. In this study, we introduce a novel atrial Laplace-Dirichlet-Rule-Based Method (LDRBM) for prescribing highly detailed myofiber orientations and providing robust regional annotation in bi-atrial morphologies of any complexity. The robustness of our approach is verified in eight extremely detailed bi-atrial geometries, derived from a sub-millimiter Diffusion-Tensor-Magnetic-Resonance Imaging (DTMRI) human atrial fiber dataset. We validate the LDRBM by quantitatively recreating each of the DTMRI fiber architectures: a comprehensive comparison with DTMRI ground truth data is conducted, investigating differences between electrophysiology (EP) simulations provided by either LDRBM and DTMRI fibers. Finally, we demonstrate that the novel LDRBM outperforms current state-of-the-art fiber models, confirming the exceptional accuracy of our methodology and the critical importance of incorporating detailed fiber orientations in EP simulations. Ultimately, this work represents a fundamental step toward the development of physics-based digital twins of the human atria, establishing a new standard for prescribing fibers in ADT. |
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75/2024 - 14/10/2024
Cattarossi, L.; Sacco, F.; Giuliani, N.; Parolini, N.; Mola, A.
A geometry aware arbitrary order collocation Boundary Element Method solver for the potential flow past three dimensional lifting surfaces | Abstract | | This work presents a numerical model for the simulation of potential flow past three dimensional lifting surfaces. The solver is based on the collocation Boundary Element Method, combined with Galerkin variational formulation of the nonlinear Kutta condition imposed at the trailing edge. A similar Galerkin variational formulation is also used for the computation of the fluid velocity at the wake collocation points, required by the relaxation algorithm which aligns the wake with the local flow. The use of such a technique, typically associated with the Finite Element Method, allows in fact for the evaluation of the solution derivatives in a way that is independent of the local grid topology. As a result of this choice, combined with the direct interface with CAD surfaces, the solver is able to use arbitrary order Lagrangian elements on automatically refined grids. Numerical results on a rectangular wing with NACA 0012 airfoil sections are presented to compare the accuracy improvements obtained by grid spatial refinement or by discretization degree increase. Finally, numerical results on rectangular and swept wings with NACA 0012 airfoil section confirm that the model is able to reproduce experimental data with good accuracy. |
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74/2024 - 08/10/2024
Crippa, B., Scotti, A.; Villa, A
A mixed-dimensional model for the electrostatic problem on coupled domains | Abstract | | We derive a mixed-dimensional 3D-1D formulation of the electrostatic equation in two domains with different dielectric constants to compute, with an affordable computational cost, the electric field and potential in the relevant case of thin inclusions in a larger 3D domain. The numerical solution is obtained by Mixed Finite Elements for the 3D problem and Finite Elements on the 1D domain. We analyze some test cases with simple geometries to validate the proposed approach against analytical solutions, and perform comparisons with the fully resolved 3D problem. We treat the case where ramifications are present in the one-dimensional domain and show some results on the geometry of an electrical treeing, a ramified structure that propagates in insulators causing their failure. |
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73/2024 - 07/10/2024
Liverotti, L.; Ferro, N.; Soli, L.; Matteucci, M.; Perotto, S.
Using SAR Data as an Effective Surrogate for Optical Data in Nitrogen Variable Rate Applications: a Winter Wheat Case Study | Abstract | | This study highlights the feasibility of using SAR data as a surrogate for optical acquisitions in the generation of nitrogen prescription maps in wheat cultivation. Unlike the optical-based approaches which are negatively affected by adverse meteorological conditions, the proposed strategy provides the possibility to compute the fertilization maps at any date, by exploiting the all-weather, day-and-night SAR capabilities. We train a U-Net-like CNN architecture on Sentinel-2 optical and Sentinel-1 SAR datasets, after a properly alignment in time. The trained model returns a surrogate NDVI distribution starting from SAR acquisitions, when optical data are not available. The recovered NDVI information is converted into LAI and GAI distributions, by resorting to an exponential and a linear law, respectively, according to the literature. Finally, the nitrogen prescription map is obtained out of the recovered GAI values. A qualitative and quantitative analysis of the error between the optical and SAR-derived prescription maps shows that the procedure is accurate, especially during the tillering and the stem elongation growth phases. |
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72/2024 - 26/09/2024
Patanè, G.; Bortolotti, T.; Yordanov, V.; Biagi, L. G. A.; Brovelli, M. A.; Truong, A. Q; Vantini, S.
An interpretable and transferable model for shallow landslides detachment combining spatial Poisson point processes and generalized additive models | Abstract | | Less than 10 meters deep, shallow landslides are rapidly moving and strongly dangerous slides. In the present work, the probabilistic distribution of the landslide detachment points within a valley is modelled as a spatial Poisson point process, whose intensity depends on geophysical predictors according to a generalized additive model. Modelling the intensity with a generalized additive model jointly allows to obtain good predictive performance and to preserve the interpretability of the effects of the geophysical predictors on the intensity of the process. We propose a novel workflow, based on Random Forests, to select the geophysical predictors entering the model for the intensity. In this context, the statistically significant effects are interpreted as activating or stabilizing factors for landslide detachment. In order to guarantee the transferability of the resulting model, training, validation, and test of the algorithm are performed on mutually disjoint valleys in the Alps of Lombardy (Italy). Finally, the uncertainty around the estimated intensity of the process is quantified
via semiparametric bootstrap. |
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71/2024 - 19/09/2024
Zhang, L.; Pagani, S.; Zhang, J.; Regazzoni, F.
Shape-informed surrogate models based on signed distance function domain encoding | Abstract | | We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the computational domain. Our approach is based on the combination of two neural networks (NNs). The first NN, conditioned on a latent code, provides an implicit representation of geometry variability through signed distance functions. This automated shape encoding technique generates compact, low-dimensional representations of geometries within a latent space, without requiring the explicit construction of an encoder. The second NN reconstructs the output physical fields independently for each spatial point, thus avoiding the computational burden typically associated with high-dimensional discretizations like computational meshes. Furthermore, we show that accuracy in geometrical characterization can be further enhanced by employing Fourier feature mapping as input feature of the NN. The meshless nature of the proposed method, combined with the dimensionality reduction achieved through automatic feature extraction in latent space, makes it highly flexible and computationally efficient. This strategy eliminates the need for manual intervention in extracting geometric parameters, and can even be applied in cases where geometries undergo changes in their topology. Numerical tests in the field of fluid dynamics and solid mechanics demonstrate the effectiveness of the proposed method in accurately predict the solution of PDEs in domains of arbitrary shape. Remarkably, the results show that it achieves accuracy comparable to the best-case scenarios where an explicit parametrization of the computational domain is available. |
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68/2024 - 16/09/2024
Gambarini, M.; Ciaramella, G.; Miglio, E.
A gradient flow approach for combined layout-control design of wave energy parks | Abstract | | Wave energy converters (WECs) represent an innovative technology for power generation from renewable sources (marine energy). Although there has been a great deal of research into such devices in recent decades, the power output of a single device has remained low. Therefore, installation in parks is required for economic reasons. The optimal design problem for parks of WECs is challenging since it requires the simultaneous optimization of positions and control parameters. While the literature on this problem usually considers metaheuristic algorithms, we present a novel numerical framework based on a gradient-flow formulation. This framework is capable of solving the optimal design problem for WEC parks. In particular, we use a low-order adaptive Runge-Kutta scheme to integrate the gradient-flow equation and introduce an inexact solution procedure. Here, the tolerances of the linear solver used for projection on the constraint nullspace and of the time-advancing scheme are automatically adapted to avoid over-solving so that the method requires minimal tuning. We then provide the specific details of its application to the considered WEC problem: the goal is to maximize the average power produced by a park, subject to hydrodynamic and dynamic governing equations and to the constraints of available sea area, minimum distance between devices, and limited oscillation amplitude around the undisturbed free surface elevation. A suitable choice of the discrete models allows us to compute analytically the Jacobian of the state problem's residual. Numerical tests with realistic parameters show that the proposed algorithm is efficient, and results of physical interest are obtained.
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